Explanation
To write a number as product of its primes, we divide it by various prime numbers $$ 2, 3, 5, 7 $$ etc one by one and check by which prime numbers it is divisible with and how many times.
Hence, $$ 20 = 2 \times 10 = 2 \times 2 \times 5 $$
The decimal expansion of a number is terminating if the denominator of the number can be expressed in the form of $$2^m\times 5^n$$ where $$m$$ and $$n$$ are non-negative integers
A) $$\dfrac{77}{210},$$ prime factorisation of the denominator is given as
$$210=2\times 3\times 5\times 7$$
$$\implies$$ denominator is not of the form $$2^m \times 5^n $$
B) $$\dfrac{23}{30},$$ prime factorisation of the denominator is given as
$$30=2\times 3\times 5$$
C) $$\dfrac{125}{441},$$ prime factorisation of the denominator is given as
$$441=21^2$$
D) $$\dfrac{23}{8},$$ prime factorisation of the denominator is given as
$$8=2^3$$
$$\implies$$ denominator is of the form $$2^m \times 5^n $$ where $$m=3$$ and $$n=0$$
Hence the decimal expansion of $$\dfrac{23}{8}$$ is terminating
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